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Talk:2017 Spring Event/@comment-31667592-20170404133413/@comment-31421201-20170405111300
Yay, a math thread! For the bronze chest the Expected Value (i.e. number of daily specials per chest on average) is EBronze = 0.07 + 0.2 x (70/40) x EBronze That is, we get 0.07 daily specials, plus a 0.2 chance to get 70 lanterns which is 70/40=1.75 new chests that have the same expected value. This may seem circular, but we can juggle this around using basic math to make more sense. First we simplify 0.2 x (40/70) = 0.2 x 1.75 = 0.35 so we get EBronze = 0.07 + 0.35 x EBronze Subtract 0.35 x EBronze from both sides to get (1 - 0.35) x EBronze = 0.07 1-0.35 = 0.65 so lets divide both sides with that. On the left side they cancel out so we get EBronze = 0.07 / 0.65 which is 0.307692...etc Using the same math for the gold chest we get EGold = 0.25 + 0.2 x (200/120) x EGold = 0.375 0.2 x (200/120) = 0.333333.... or 1/3 so EGold = 0.25 + EGold/3 (1 - 1/3) x EGold = 0.25 (2/3) x EGold = 0.25 EGold = 0.25 / (2/3) = 0.375 Ok, so that was surprisingly close to the bronze chest. Given infinite attempts it won't be a huge difference. So far they seem comparable. If we add in the average lanters from chest trees they get a bit closer still, although that math gets a bit long winded. However, 7% is a wholly different beast than 25%. Lets say we have 1200 lanterns to spend. That's 30 bronze chests or 10 gold chests. Lets further assume that each bronze chest becomes 1.35 chests due to the lantern reward as per the math above, and gold chests become 1.3333 chests. So in the end we get 40.5 bronze chests and 13.3 gold chests. Lets round that to 41 and 13 respectively. What is the probability that you open all these chests and dont get the daily special? For bronze that is (1-0.07) ^ 41 = 0.051. So when opening 41 chests theres about one in twenty players that will get zero daily specials. Out of 100,000 players about 5100 players would be really really disapointed. Now lets check the same if we instead invested in gold chests. (1-0.25)^13 = 0.0238. Thats less than half of the "unlucky chance" of bronze chests (about one in 42). Gold chests are more consistent not-complete-failure. Out of 100,000 players that invest in gold chests instead, "only" 2376 players were supremely pissed. As a last point, that may or may not be of interest, when NOT getting the daily special, and NOT getting more lanterns, what do you get? The failure states of the gold chest are far more valuable than the bronze chest. The Spring event is described as "annual" in several ingame texts, so there are good odds that it will return next year. My personal strategy is to go only for gold chests, because even if I fail it gain something of value.